1. ## Derivative of 1/cot

$\int{\frac{d{\theta}}{cot{\theta}}$

The question was to solve the ODE

$cot{\theta}d{\rho} + {\rho}d{\theta}=0$

I was solving using variable separable and got to a point

$\int{\frac{d{\rho}}{{\rho}} + \int{\frac{d{\theta}}{cot{\theta}} = \int{0}$

2. $\int \dfrac{d\theta}{\cot \theta}=\int\dfrac{\sin \theta}{\cos \theta}d\theta=-\log |\cos \theta|+C$